Analysis of multiple stiffened barrel shell structures by strain-based finite elements

In this paper strain-based rectangular cylindrical shell and curved arch finite elements are coupled to straight beam finite elements to analyse multiple stiffened barrel shell structures. The first two finite elements are based on assumed strains rather than displacement fields. The results obtained with this analysis are successfully compared with values derived from several commercial computer codes.     

Numerical solution of curved pipes submitted to in-plane loading conditions

An alternative formulation to current meshes dealing with finite shell elements is presented to solve the problem of stress analysis of curved pipes subjected to in-plane bending forces. The solution is based on finite curved elements, where displacements are defined from a total set of trigonometric functions or a fifth-order polynomial, combined with Fourier series. Global shell displacements are achieved through the one associated with curved arch bending and the other referred to the toroidal thin-walled shell distortion. Beam-type displacement and in-plane rotation are uncoupled and separately formulated, using trigonometric shape functions, as in Timoshenko or Mindlin beam theory. To build up the solution, a simple deformation model was adopted, based on the semi-membrane concept of the doubly curved shells behaviour. Several studies are presented and compared with experimental and numerical analyses reported by other authors.     

面内加载时弯管的数值计算方法

对平面内弯矩作用下的弯管的应力分析提出了一种新的计算方法,以替代现行的有限元网格法。新方法的提出基于有限弯曲单元,其位移由一系列三角函数或者五次多项式,与傅里叶级数共同计算而得。整体的壳位移由两类位移组合而成,一个是拱的弯曲位移,另一个则是环形的薄壁壳体的翘曲位移。梁模型的位移和平面内转角是不耦合的,分别应用三角函数,如Timoshenko或Mindlin梁理论计算得到。基于双曲线壳体的半膜单元概念,提出了一个简化的变形模型用于此计算方法。研究成果也与已有的试验和数值分析结果进行了对比。     

Recent advances in local–global FE analysis of shells of revolution

A local–global finite element technique, suitable for the analysis of shells of revolution with localized non-axisymmetric effects such as cracks, cutouts and column supports, is presented. Both material and geometrical nonlinearities are considered. The model combines, in a single analysis, rotational shell elements, general shell elements, and column elements. Rotational shell elements are employed in the axisymmetric portion of the shell, where the nonaxisymmetric behaviour in loading and deformation is accounted for by including appropriate Fourier harmonics. In the local zone, where deviations from axisymmetry are contained, a general isoparametric shell element is employed. Continuity of displacements between the rotational and general shell elements is achieved either by a layer of transitional elements or by a direct coordinate transformation. If the shell is supported on a discrete system of columns , a standard 3-D beam element with six degrees-of-freedom per node is deployed. This local–global approach has been applied to a wide variety of shell problems.     

Triangular higher-order element for better prediction of stress resultants and stresses in plated and shell structures

Although they furnish accurate displacements, conventional displacement-based lower order finite elements fail to predict accurate stress resultants and stresses in certain classes of plate and shell problems that involve free edges, steep stress gradients and singularities. In order to tackle such problems, a triangular higher-order shell element based on the nodal basis approach has been developed. The nodes of the element are located at optimal points and its more superior shape functions derived from orthogonal Proriol polynomials. To illustrate the improved performance of the higher-order element as compared to commonly used lower order shell elements in predicting the variations of stress resultants and stresses, three example problems involving a simply supported skew plate, a corner supported square plate, and a clamped cylindrical shell are solved. The stress resultants and the stresses furnished by the higher-order element for the problems considered are found to be accurate with the satisfaction of the natural boundary conditions and devoid of any oscillations. When compared to lower order elements, the higher-order element requires a simple mesh design and lesser degrees of freedom resulting in a considerable reduction in the computational effort, especially for large scale nonlinear analysis.     

Free vibrations of fluid-filled cylindrical shells on elastic foundations

The free vibration characteristics of fluid-filled cylindrical shells on elastic foundations are presented by a semi-analytical finite element method. A shell is discretized into cylindrical finite elements where shell governing equations based shape functions in the longitudinal direction are used instead of the usual simple polynomials. Non-uniformities of the foundations in the circumferential and longitudinal directions are handled by the Fourier series and an element mesh strategy, respectively. The fluid domain is described by the potential flow theory. The hydrodynamic pressure acting on shells is derived from the condition for dynamic coupling of the fluid-structure. The effect of fluid in a shell, shell geometries, and foundation parameters on the dynamic behavior of fluid-containing shells is investigated. Numerical results based on the present method converge more rapidly than those obtained by the simple polynomial formulation. The method is suitable for the problem considered due to its generality, simplicity, and potential for further development.     

采用新型阻尼杆的双层柱面网壳结构减震分析与试验研究

为了检验用新型阻尼杆件替换网壳结构部分杆件后的减震效果,设计了适合网壳结构的新型孔隙式粘滞阻尼杆,在拟动力装置上进行了新型孔隙式粘滞阻尼杆的性能测试。在此基础上设计制作了双层柱面网壳结构模型,进行了新型阻尼器杆件替换网壳杆件减震的振动台试验。在替换杆件不多的情况下,各点的位移、加速度和内力减震60%左右,说明新型孔隙式粘滞阻尼杆减震策略有效、可行。理论分析和试验结果较为接近,最大误差10%。     

Interaction between laser-welded web-core sandwich deck plate and girder under bending loads

Present paper investigates the interaction between laser-welded web-core sandwich deck plate and supporting girder under bending loads. The study is based on two linear-elastic Finite Element (FE) approaches, i.e. one using beam elements to model the girder and shell elements to model the homogenized web-core sandwich plate. With this approach the obtained FE model is considerably smaller than in the case of modeling the full, periodic, 3D geometry with shell elements. The FE solution results in stress resultants for beam and shell elements. These stress resultants do not describe accurately the periodic stress response of the sandwich plate or shear stress distribution at girder web. Therefore, the paper utilizes analytical methods to calculate these stress components from the obtained Finite Element solution. The second computational approach is based on modeling the actual 3D topology with shell elements. The two approaches are shown to be in very good agreement. The investigation shows that the effective flange width of the sandwich is different for the top and bottom face plates indicating that the interaction is different for these face plates. The present study also shows that this difference between the two faces depends strongly on the orientation of the web plates of the sandwich with respect to girder axis and the stiffness of the girder. The investigation also shows that the normal stress response in bending is dominated by the interaction between the sandwich plate and the girder, but also by the shear-induced normal stresses at the outer surface of the plate.     

The strain approach to the development of thin cylindrical shell finite elements

The method of forming thin cylindrical shell finite element displacement functions by initially developing the strain function is presented. The Kirchhoff-Love assumptions are used together with deep thin shell finite elements to develop a number of 20 degrees-of-freedom rectangular and 15 degrees-of-freedom triangular cylindrical shell elements. The elements are tested on an extended range of barrel vault roof problems and results are presented. Only in the very specific case of N_φ for the free straight-edged barrel vault using the triangular elements are the results found to be inaccurate. In all cases where the displacements and stresses can be analytically checked, the strain approach gives accurate results.     

空间钢框架高等分析的塑性区方法研究

钢框架结构高等分析的塑性区模型能够精确地模拟结构二阶非弹性性能,在对基于构件截面弯矩-曲率-轴力关系的塑性区模型和基于有限单元法实体单元、壳单元及纤维单元的塑性区模型进行系统研究之后,指出它们的优缺点及应用过程中需要注意的问题。并在此基础上,介绍基于塑性区模型的混合单元技术,为进行塑性区模型的理论研究及应用提供依据,同时为空间钢框架结构的精确非线性分析提供参考。     

Numerical Modelling of Thin-Walled Stainless Steel Structural Elements in Case of Fire

In this paper, the structural response of stainless steel thin-walled elements submitted to fire is analysed numerically by means of the geometrically and materially non-linear Finite Element program SAFIR, including imperfections. In order to make these simulations, two main changes in the program were made: (i) the code was changed in order to deal with the stainless steel 2D material constitutive law to be used with shell elements and (ii) the possibility of the program to take into account residual stresses with shell finite elements was introduced. The stainless steel stress–strain relationship at high temperatures was based on the one presented in part 1.2 of Eurocode 3. To model the strain hardening exhibited by the stainless steels, using the shell element formulation, an approximation to the Eurocode 3 constitutive law was needed. Local and global geometrical imperfections were considered in the simulations. The paper shows the influence of the residual stresses on the ultimate load-carrying capacity of thin-walled stainless steel structural elements in case of fire.     

膜板壳理论及其在结构分析软件中的应用

介绍了膜板壳理论,在此基础上结合三种常用结构分析软件SATWE,ETABS和SAP,说明了膜板壳单元是如何被应用的,分析了用膜板壳单元来模拟楼板,剪力墙时应该注意的事项,为准确利用这三种软件进行结构分析以及进行相互对比提供了参考.     

单点连续冲击荷载下单层球面网壳结构失效模式研究

为研究单点连续冲击荷载作用下单层球面网壳结构的失效模式,应用通用有限元软件ANSYS LS-DYNA建立了40m跨度,四种不同矢跨比的K8型单层球面网壳结构有限元模型。通过分析单层球面网壳结构在单点连续冲击荷载作用下失效全过程的冲击荷载、能量转化和杆件变形特点,总结归纳出单层球面网壳结构在单点连续冲击荷载作用下的五种失效模式:网壳局部凹陷、网壳局部凹陷时杆件剪切破坏、网壳整体塌陷、网壳整体塌陷时杆件剪切破坏、杆件剪切破坏。对五种失效模式进行了全过程研究分析,明确了单层球面网壳结构在单点连续冲击全过程中肋杆、环杆、斜杆的破坏形式和能量传递与转化特点。     

中庭结构的抗震设计

本文结合工程实例，对中庭结构的受力特点进行分析。采用了三维空间杆系分析程序和壳元板元的空间有限元分析程序，经过比较，得出了壳元模拟弹性楼板计算方案，对中庭结构体系的分析更为合理的结论。本文为大型商业建筑中庭的结构布置及其计算程序的选用提供参考。     

Beam and shell element model for advanced analysis of steel structural members

Plastic zone method of advanced analysis, which uses shell elements to model the entire structure, is the most accurate method available to predict the ultimate strength and behavior of steel frames. The disadvantage of such full shell plastic zone models is that it is computationally expensive and hence its use is limited to small structures. Beam elements in commercial finite element packages can model residual stress and capture spread of plasticity, but cannot model local buckling of plates that the member is made up of, which leads to unloading and failure in steel frames. A hybrid model using shell elements only in the regions vulnerable to elastic or inelastic local buckling and beam elements in other locations could overcome this limitation of full beam element model. The issues in using this hybrid model are, knowing a priori the location and length of the shell element region and connecting the beam and shell regions without any artificial stress concentrations or incompatible displacements. In this study, in addition to addressing these issues, the hybrid model is systematically evaluated by studying its performance in structural elements. It is seen that the hybrid model strength predictions has an average error of only 0.91% but requires on an average 83% less computational time when compared to the full shell plastic zone models.     

Beam and shell element model for advanced analysis of steel structural members

Plastic zone method of advanced analysis, which uses shell elements to model the entire structure, is the most accurate method available to predict the ultimate strength and behavior of steel frames. The disadvantage of such full shell plastic zone models is that it is computationally expensive and hence its use is limited to small structures. Beam elements in commercial finite element packages can model residual stress and capture spread of plasticity, but cannot model local buckling of plates that the member is made up of, which leads to unloading and failure in steel frames. A hybrid model using shell elements only in the regions vulnerable to elastic or inelastic local buckling and beam elements in other locations could overcome this limitation of full beam element model. The issues in using this hybrid model are, knowing a priori the location and length of the shell element region and connecting the beam and shell regions without any artificial stress concentrations or incompatible displacements. In this study, in addition to addressing these issues, the hybrid model is systematically evaluated by studying its performance in structural elements. It is seen that the hybrid model strength predictions has an average error of only 0.91% but requires on an average 83% less computational time when compared to the full shell plastic zone models.     

Isogeometric cohesive zone model for thin shell delamination analysis based on Kirchhoff-Love shell model

We present a cohesive zone model for delamination in thin shells and composite structures. The isogeometric (IGA) thin shell model is based on Kirchhoff-Love theory. Non-Uniform Rational B-Splines (NURBS) are used to discretize the exact mid-surface of the shell geometry exploiting their C¹-continuity property which avoids rotational degrees of freedom. The fracture process zone is modeled by interface elements with a cohesive law. Two numerical examples are presented to test and validate the proposed formulation in predicting the delamination behavior of composite structures.     

The effects of interfacial strength on fractured microcapsule

The effects of interfacial strength on fractured microcapsule are investigated numerically. The interaction between crack and microcapsule embedded in mortar matrix is modeled based on cohesive approach. The microcapsules are modelled with variation of core-shell thickness ratio and potential cracks are represented by pre-inserted cohesive elements along the element boundaries of the mortar matrix, microcapsules core, microcapsule shell, and at the interfaces between these phases. Special attention is given to the effects of cohesive fracture on the microcapsule interface, namely fracture strength, on the load carrying capacity and fracture probability of the microcapsule. The effect of fracture properties on microcapsule is found to be significant factor on the load carrying capacity and crack propagation characteristics. Regardless of core-shell thickness ratio of microcapsule, the load carrying capacity of self-healing material under tension increases as interfacial strength of microcapsule shell increases. In addition, given the fixed fracture strength of the interface of microcapsule shell, the higher the ratio core-shell thickness, the higher the probability of microcapsules being fractured.     

CFRP Effect on the Buckling Behavior of Dented Cylindrical Shells

Considering that the use of thin-walled shells is expanding every day, it is important to examine the problem of instability in this form of structure. Many steel structures such as high-water tanks, water and oil reservoirs, marine structures, and pressure vessels, including shell elements, are under stress tension. In addition, shell elements are subject to instability owing to the loads applied. Ten thin-walled cylindrical shell specimens in two groups with different dent depths of t_c and 2t_c, and the different dent number subject to uniform external pressure were tested in the present research (t_c is the thickness of cylindrical shell). The samples were modified to include either one or two dent line with amplitudes of h/3 in height (h the height of cylinder shell). Moreover, CFRP Strips on the dent depth was used in one of the groups. The results of testing under different theories and codes are compared.

     

Finite element techniques for the analysis of cooling tower shells with geometric imperfections

Two finite element methods for analysing geometrically imperfect cooling tower shells are presented. In the first the geometry of the imperfection is modelled by the elements; in the second the imperfection is represented by an equivalent load on the shell. Axisymmetric and general shell elements have been considered.Results are given which show that the first approximation to the equivalent load is sufficiently accurate and that it is possible to represent local imperfections by axisymmetric imperfections which require less computation. It is also shown that axisymmetric elements should be used wherever possible, because of their greater efficiency, following the geometry of an axisymmetric imperfection but representing local imperfections by equivalent loads.